Transcript 4.1 Ratio and Proportion • Ratio – comparison of two numbers by division. – Can be written: • a to b • a:b • a b where b.

4.1 Ratio and Proportion
• Ratio – comparison of two numbers by division.
– Can be written:
• a to b
• a:b
•
a
b
where b ≠ 0.
• If a and b represent quantities measured in
different units, then the ratio of a to b is a rate.
• A unit rate is a rate with a denominator of 1.
– Ex.
40miles
1hour
Using Unit Rates
Find the rate (cost per ounce).
$.72
 $.045/ oz
16oz
$1.20
 $.0375 / oz
32oz
$1.60
 $.025/ oz
64oz
Converting Rates
A cheetah ran 300 feet in 2.92 seconds. What was the
cheetah’s speed in miles per hour?
You need to convert feet to miles and seconds to hours.
300 ft
1mi
60s 60 min



2.92s 5280 ft 1min
1h
300 ft
1mi
60s 60 min




2.92s 5280 ft 1min
1h
1080000

 70mi / h
15417.6
Solving Proportions
• A proportion is an equation that states that two
ratios are equal.
a = c for b ≠ 0 and d ≠ 0.
b
d
You read this proportion as “a is to b as c is to d”.
• The extremes of the proportion – are a and d.
• The means of the proportion – are b and c.
• Another way you can see this proportion written
is a : b = c : d.
Cross Products
• The products ad and bc are the cross products of the
a c
proportion  .
b
• For example,
d
2 8

3 12
2  12  8  3
Using Cross Products
y
3
• Use cross products to solve the proportion
 .
2.5
4
y
3

2.5
4
y(4)  (2.5)( 3)
4 y  7.5
y  1.875
Using Multi-Step Proportions
• Solve the proportion x  4 x  2

.
5
7
x4 x2

5
7
7( x  4)  5( x  2)
7 x  28  5 x  10
2 x  28  10
2 x  38
x  19
More Practice!!!!
• Textbook – p. 185 #2 – 28 even, p. 186
#32 – 36 even.
• Homework – Worksheet 4.1